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Simplifying y2 + 11y = 6 Reorder the terms: 11y + y2 = 6 Solving 11y + y2 = 6 Solving for variable 'y'. Reorder the terms: -6 + 11y + y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 11y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 11y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 11y + y2 = 0 + 6 11y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 11y + y2 = 6 The y term is 11y. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11y + 30.25 + y2 = 6 + 30.25 Reorder the terms: 30.25 + 11y + y2 = 6 + 30.25 Combine like terms: 6 + 30.25 = 36.25 30.25 + 11y + y2 = 36.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (y + 5.5) equal to 6.020797289 and -6.020797289.Subproblem 1
y + 5.5 = 6.020797289 Simplifying y + 5.5 = 6.020797289 Reorder the terms: 5.5 + y = 6.020797289 Solving 5.5 + y = 6.020797289 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 6.020797289 + -5.5 y = 6.020797289 + -5.5 Combine like terms: 6.020797289 + -5.5 = 0.520797289 y = 0.520797289 Simplifying y = 0.520797289Subproblem 2
y + 5.5 = -6.020797289 Simplifying y + 5.5 = -6.020797289 Reorder the terms: 5.5 + y = -6.020797289 Solving 5.5 + y = -6.020797289 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -6.020797289 + -5.5 y = -6.020797289 + -5.5 Combine like terms: -6.020797289 + -5.5 = -11.520797289 y = -11.520797289 Simplifying y = -11.520797289Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.520797289, -11.520797289}
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